Three Dimensional Geometry questions
879 published questions with worked solutions.
- Let P(x, y, z) be a point in the first octant, whose projection in the xy-plane is the point Q. Let OP = γ; the angle between OQ...
- If the equation of a plane P, passing through the intersection of the planes, x + 4y – z + 7 = 0 and 3x + y + 5z = 8 is ax + by +...
- The distance of the point (1, –2, 3) from the plane x – y + z = 5 measured parallel to the line x 2 = y 3 = z -6 is :
- If (a, b, c) is the image of the point (1, 2, – 3) in the line, x+1 2 = y-3 -2 = z -1 , then a + b + c is equal to
- If for some R, the lines L_1: x+1 2 = y-2 -1 = z-1 1 and L_2: x+2 = y+1 5- = z+1 1 are coplanar, then the line L_2 passes through...
- A plane P meets the coordinate axes at A, B and C respectively. The centroid of ABC is given to be (1, 1, 2). Then the equation...
- Let z_1,z_2,z_3 be three complex numbers satisfying 1 z_1 + 1 z_2 + 1 z_3 =0. Let z_k=r_k( _k+i _k) and _k= 2 _k+i 2 _k z_k for...
- Let the point A be the foot of perpendicular drawn from the point P(a, b, 0) on the line x-1 2 = y-2 1 = z- 3 . If the midpoint...
- If the point of intersection of the lines x + 1 3 = y + a 5 = z + b + 1 7 and x - 2 1 = y - b 4 = z - 2a 7 lies on xy-plane, then...
- Let a line L passing through the point (1, 1, 1) be perpendicular to both the vectors 2î + 2ĵ + k̂ and î + 2ĵ + 2k̂. If P(a, b,...
- A line with direction ratios 1, −1, 2 intersects the lines x2 = y3 = z+1 3 and x+1 -1 = y-2 1 = z4 at the points P and Q,...
- The square of the distance of the point (−2, −8, 6) from the line x-1 1 = y-1 2 = z -1 along the line x+5 1 = y+5 -1 = z2 is...
- If (2 +1, ^2-3 , -1 2 ) is the image of (α, 2α, 1) in the line x-2 3= y-1 2= z1, then the possible value(s) of α is (are)
- Let a triangle PQR be such that P and Q lie on the line x+3 8= y-4 2= z+1 2 and are at a distance of 6 units from R(1,2,3). If...
- If the distance of the point (a,2,5) from the image of the point (1,2,7) in the line x1= y-1 1= z-2 2 is 4, then the sum of all...
- The square of the distance of the point P(5,6,7) from the line x-2 2= y-5 3= z-2 4 is equal to:
- The square of the distance of the point of intersection of the lines r=( i+ j- k)+ (a i- j), a≠0 and r=(4 i- k)+ (2 i+a k) from...
- Let the image of the point P(0,−5,0) in the line x-1 2= y1= z+1 -2 be the point R and the image of the point Q(0,−1/2,0) in the...
- Let the image of the point P(1, 6, a) in the line L: x1= y-1 2= z-a+1 b, b>0, be ( a3, 0, a+c ). If S(α, β, γ), α>0, is the point...
- Let a line L be perpendicular to both the lines L_1: x+1 3= y+3 5= z+5 7 and L_2: x-2 1= y-4 4= z-6 7. If θ is the acute angle...
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